# Multiplying and dividing using scientific notation

## Multiplying & dividing in scientific notation

Intermediate Algebra Skill. Multiplying and Dividing Using Scientific Notation. Simplify. Write each answer in scientific notation. 1) ( ? 10?6)( ? 10?5).

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If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Math Pre-algebra Exponents, radicals, and scientific notation Computing with scientific notation. Multiplying in scientific notation example. Multiplying three numbers in scientific notation. Current timeTotal duration

In order to understand this lesson, you will need to have a basic understanding of scientific notation. Throughout your studies, you may be asked to multiply or divide numerals that are written in scientific notation. You will follow the same process that you learned when multiplying and dividing monomials; however, the only difference is that you will need to make sure that your final answer is written in scientific notation. Pay special attention to how we write the answer in scientific notation at the end of the problem. It can be tricky trying to figure out the exponent if the final answer is not in scientific notation format. If you have trouble thinking it through, write the initial answer in expanded form and then translate it back into scientific notation. Take a look at this final example.

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Numbers with multiple zeros can be difficult to record and manipulate. Consequently, scientists and mathematicians use a shorter method to write significantly large or small numbers called scientific notation. Instead of saying the speed of light is ,, meters per second, scientists can record it as 3. Simplifying the numbers makes them not only easier to express, but also easier to multiply. To write a number in scientific notation, you must write it as the product of a number and a power of The first number is called the coefficient, and it must be greater than or equal to 1 and less than

Quantities with exponents can be multiplied and divided easily if they have the same base. Since all number in scientific notation have base 10 , we can always multiply them and divide them. To multiply two numbers in scientific notation, multiply their coefficients and add their exponents. To divide two numbers in scientific notation, divide their coefficients and subtract their exponents. In either case, the answer must be converted to scientific notation. Here are the steps to multiply two numbers in scientific notation: Multiply the coefficients--round to the number of significant figures in the coefficient with the smallest number of significant figures. Add the exponents.

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